| Author |
 Topic  |
|
Turtle
Radio Wave
USA
45 Posts |
 Posted - 02/26/2003 : 21:28:49
In this topic people basiclly solve and give mathematical problems. When you solve a problem if would be nice to expalin how you did it so people could learn if they can't.
The first problem is: xysinyzdV
G
Where G is the rectangular box define by the inequalities 0<x< ,0<y<1,0<z</6
Turtle
Alert Mentor now
|
alis
Radio Wave
USA
88 Posts |
 Posted - 02/26/2003 : 23:17:44
Where do the parenthesis go in that?Here's a fun one that some of you have prob done before: What is the largest cardinality of a subset of  that has no limit points in ? Prove.(assume GCH if you want) ---
The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell. -St Augustine
Alert Mentor now
|
Hurkyl
Visible Light Wave
USA
723 Posts |
Posted - 02/27/2003 : 01:23:44
I haven't done that one before, but it looks neat.  The greatest cardinality is simply aleph-not. Suppose S is a subset of R with no limit points. S must have a finite number of points in any interval [n, n + 1) because otherwise it would have a limit ponit in [n, n + 1]
So, we simply divide up R into aleph-not intervals of length 1, and we're guaranteed an upper bound of aleph-not * finite = aleph-not points in S.
How hard can the questions be? I know a real doozy of an infinite sum (though it's a 2-liner if you know the trick)
Hurkyl
Alert Mentor now
|
Turtle
Radio Wave
USA
45 Posts |
Posted - 02/28/2003 : 13:02:17
Here is a easy problem, 4
 2i
i=1 Turtle
Alert Mentor now
|
pmytial
Infrared Wave
United Kingdom
418 Posts |
Posted - 02/28/2003 : 18:30:08
quote:
Originally posted by Hurkyl:How hard can the questions be? I know a real doozy of an infinite sum (though it's a 2-liner if you know the trick)
Hit us with it then
Alert Mentor now
|
Hurkyl
Visible Light Wave
USA
723 Posts |
Posted - 02/28/2003 : 22:37:46
n = 0 .. infinity arctan(1 / (1 + n + n2))Hurkyl
Alert Mentor now
|
rgrig
Radio Wave
Romania
35 Posts |
Posted - 03/06/2003 : 05:40:40
atan(a) + atan(b) = atan( (a+b) / (1-ab) )n=0..K atan( 1/ (1+n+n2) = atan(K+1) atan( ) = / 2
bye,
radu
Alert Mentor now
|
Hurkyl
Visible Light Wave
USA
723 Posts |
Posted - 03/06/2003 : 11:57:43
The partial sum is correct, but you seem to have skipped a step. [:P]Seems rgrig found the trick though. The only other way I know to solve the problem involves some fancy complex integration. Hurkyl
Alert Mentor now
|
